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Nash implementation with partially honest individuals

Dutta, Bhaskar and Sen, Arunava
(2009)
Nash implementation with partially honest individuals.
Working Paper.
Department of Economics, University of Warwick:
University of Warwick.
The Warwick Economics Research Paper Series (TWERPS), Vol.2009
(No.920).

Abstract

We investigate the problem of Nash implementation in the presence of "partially honest" individuals. A partially honest player is one who has a strict preference for revealing the true state over lying when truthtelling does not lead to a worse outcome (according to preferences in the true state) than that which obtains when lying. We show that when there are at least three individuals, the presence of even a single partially honest individual (whose identity is not known to the planner) can lead to a dramatic increase in the class of Nash implementable social choice correspondences. In particular, all social choice correspondences satisfying No Veto Power can be implemented. We also provide necessary and sufficient conditions for implementation in the two-person case when there is exactly one partially honest individual and when both individuals are partially honest. We describe some implications of the characterization conditions for the two-person case. Finally, we extend our three or more individual result to the case where there is an individual with an arbitrary small but strictly positive probability of being partially honest.